2010/01/25 by O. Gunnarsson, M. W. Haverkort, Giorgio Sangiovanni +1 · 47 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Algorithm #Applied mathematics #Computer science #Continuation #Entropy (arrow of time) #Function (biology) #Mathematics #Neural Networks and Reservoir Computing #Nonlinear Dynamics and Pattern Formation #Physics #Principle of maximum entropy #Standard deviation #Statistical error #Statistics #Systematic error #cond-mat.str-el #physics.data-an #stat.ME
paper · pdf · doi:10.1103/physrevb.81.155107
published in Physical Review B 81(15) (American Physical Society) · 10 pages and 8 figures
arxiv created 2010/01/25 · openalex publication_date 2010/04/09 · arxiv updated 2010/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic error, due to deviations of the default function, used in the MaxEnt approach, from the exact spectrum. We find that the MaxEnt approach in its classical formulation can lead to a nonoptimal balance between the two types of errors, leading to an unnecessary large statistical error. The statistical error can be reduced by splitting up the data in several batches, performing a MaxEnt calculation for each batch and averaging. This can outweigh an increase in the systematic error resulting from this approach. The output from the MaxEnt calculation can be used as a default function for a new MaxEnt calculation. Such iterations often lead to worse results due to an increase in the statistical error. By splitting up the data in batches, the statistical error is reduced and the increase resulting from iterations can be outweighed by a decrease in the systematic error. Finally we consider a linearized version to obtain a better understanding of the method.